Calculating Velocity and Angle of a Plane with Wind Gusts

[ProctorPlayer]

Homework Statement

a plane flies east @ 500km/h. a gust of wind @ 120km/h goes up at a 30 degree angle north of east. what is the velocity and angle of the plane

Homework Equations

The Attempt at a Solution

 

[Saladsamurai]

What do you know about vectors?
Did you draw a diagram?

Help us help you.

Casey

 

[ProctorPlayer]

well...

I know a little about vectors. I did draw a diagram and came very close in my drawing. Basically I had two triangles that were connected. one was a right triangle with the lower angle being 30 degrees and the other triangle was connected to that at the base and the middle angle was 150. (In accordance with the 30 degree). I used trig to get the initial velocities of both the Xworld and the Yworld. I don't know what else to say other than I asked my teacher and he said that the answer had square roots in it. hope you guys can help.

 

[slakedlime]

Are you sure it's 2 triangles or one? It would be helpful if you could post your vector drawing on the board.

If it's one triangle then you can apply the Pythagoras theorem and get the answer pretty easily. The plane would be moving east and the wind would be acting at right angles from the north. It forms a right-angled triangle.

From there you can find the resultant vector.

With the wind acting, the plane wouldn't be flying straight east but as a resultant. Then you can find the angle, which should be its deviation from the path due east.

I might be wrong; if you could post your diagram it'd be a big help. :)